论文标题
集体性和更高的集成性；更高的Cheeger-Simons和Godbillon-Veyvey不变
Bott Integrability and Higher Integrability; Higher Cheeger-Simons and Godbillon-Vey Invariants
论文作者
论文摘要
本文研究了$ C^\ infty $歧管$ m $的$π_1（m）$与Bott对集成性的原始障碍物的相互作用，以及差异的几何不变性（例如Godbillon-vey和Cheeger-Simons of Fortianiants of Fortianiants）的相互作用。我们证明，较高的pontrjagin和更高的Chern类的戒指是一个可集成的子包裹的$ e $ e $的歧管的切线捆绑包，而歧管上的$ 2k $ $ k = dim（tm/e）$，而较高的pontrjagin和chern环是由$ i^*y \ cup p _ y y y y y \ y \ y i i^y y y y y y y i i^y y y y y i i i^* c_j（tm/e）$，分别为$ p_j $ $ j $ -th pontrjagin类，$ c_j $ $ j $ - j $ -th chern class，$ i：m \ tobπ$和$π=π_1（bg）$ $ bg $的集团满足了诺维科夫的猜想。此外，我们还显示了由$ i^*x \ cup p_j（tm/e）$以及$ i^*x \ cup c_j（tm/e）$产生的较高pontrjagin和Chern Rings的消失，如前Folied Novikov的猜想，其中$ \ Mathcal {F} $是叶面，其切线束为$ e $。我们举例说明了这种障碍以及更高的Godbillon-Vey和Cheeger-Simons不变。
This paper studies the interaction of $π_1(M)$ for a $C^\infty$ manifold $M$ with Bott's original obstruction to integrability, and with differential geometric invariants such as Godbillon-Vey and Cheeger-Simons invariants of a foliation. We prove that the ring of higher Pontrjagin and higher Chern classes of an integrable subbundle $E$ of the tangent bundle of a manifold vanishes above dimension $2k$ where $k=dim(TM/E)$, and where the higher Pontrjagin and Chern rings are rings generated by $i^*y \cup p_j(TM/E)$ and by $i^*y \cup c_j(TM/E)$ respectively, with $p_j$ the $j$-th Pontrjagin class, $c_j$ the $j$-th Chern class, $i:M \to Bπ$ and $π=π_1(BG)$, where $BG$ is the classifying space of the holonomy groupoid corresponding to $E$ and $y \in H^*(Bπ)$, provided that the fundamental group of $BG$ satisfies the Novikov conjecture. In addition, we show the vanishing of higher Pontrjagin and Chern rings generated by $i^*x \cup p_j(TM/E)$, and by $i^*x \cup c_j(TM/E)$ as before but with $i:M \to BG$, $BG$ as above and $x \in H^*(BG)$ provided $(M,\mathcal{F})$ satisfied the foliated Novikov conjecture, where $\mathcal{F}$ is the foliation whose tangent bundle is $E$. We give examples of this obstruction and of higher Godbillon-Vey and Cheeger-Simons invariants.
